Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2128,2,Mod(1,2128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2128, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2128.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2128 = 2^{4} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2128.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(16.9921655501\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{21}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 532) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.79129\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2128.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.79129 | 1.61155 | 0.805775 | − | 0.592221i | \(-0.201749\pi\) | ||||
0.805775 | + | 0.592221i | \(0.201749\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 4.79129 | 1.59710 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.79129 | 1.14312 | 0.571558 | − | 0.820562i | \(-0.306339\pi\) | ||||
0.571558 | + | 0.820562i | \(0.306339\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.00000 | −0.277350 | −0.138675 | − | 0.990338i | \(-0.544284\pi\) | ||||
−0.138675 | + | 0.990338i | \(0.544284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.37386 | 2.16212 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.79129 | 0.919522 | 0.459761 | − | 0.888043i | \(-0.347935\pi\) | ||||
0.459761 | + | 0.888043i | \(0.347935\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.79129 | −0.609109 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.58258 | −0.955533 | −0.477767 | − | 0.878487i | \(-0.658554\pi\) | ||||
−0.477767 | + | 0.878487i | \(0.658554\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | 0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.79129 | 0.704024 | 0.352012 | − | 0.935995i | \(-0.385498\pi\) | ||||
0.352012 | + | 0.935995i | \(0.385498\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.37386 | −1.32438 | −0.662192 | − | 0.749334i | \(-0.730374\pi\) | ||||
−0.662192 | + | 0.749334i | \(0.730374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 10.5826 | 1.84219 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.00000 | −0.507093 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.00000 | 0.821995 | 0.410997 | − | 0.911636i | \(-0.365181\pi\) | ||||
0.410997 | + | 0.911636i | \(0.365181\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.79129 | −0.446964 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.79129 | −0.592100 | −0.296050 | − | 0.955172i | \(-0.595669\pi\) | ||||
−0.296050 | + | 0.955172i | \(0.595669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | −0.304997 | −0.152499 | − | 0.988304i | \(-0.548732\pi\) | ||||
−0.152499 | + | 0.988304i | \(0.548732\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 14.3739 | 2.14273 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −10.5826 | −1.54363 | −0.771814 | − | 0.635849i | \(-0.780650\pi\) | ||||
−0.771814 | + | 0.635849i | \(0.780650\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10.5826 | 1.48186 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.37386 | −1.15024 | −0.575119 | − | 0.818070i | \(-0.695044\pi\) | ||||
−0.575119 | + | 0.818070i | \(0.695044\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.3739 | 1.53365 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.79129 | −0.369715 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.1652 | −1.58377 | −0.791884 | − | 0.610672i | \(-0.790900\pi\) | ||||
−0.791884 | + | 0.610672i | \(0.790900\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.00000 | −0.128037 | −0.0640184 | − | 0.997949i | \(-0.520392\pi\) | ||||
−0.0640184 | + | 0.997949i | \(0.520392\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.79129 | −0.603646 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.00000 | −0.372104 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.37386 | 1.14520 | 0.572600 | − | 0.819835i | \(-0.305935\pi\) | ||||
0.572600 | + | 0.819835i | \(0.305935\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −12.7913 | −1.53989 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1652 | 1.44374 | 0.721869 | − | 0.692030i | \(-0.243283\pi\) | ||||
0.721869 | + | 0.692030i | \(0.243283\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.3739 | 1.91642 | 0.958208 | − | 0.286073i | \(-0.0923499\pi\) | ||||
0.958208 | + | 0.286073i | \(0.0923499\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.1652 | 1.28924 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.79129 | −0.432057 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.0000 | 1.12509 | 0.562544 | − | 0.826767i | \(-0.309823\pi\) | ||||
0.562544 | + | 0.826767i | \(0.309823\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.417424 | −0.0463805 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.3739 | −1.57774 | −0.788868 | − | 0.614562i | \(-0.789333\pi\) | ||||
−0.788868 | + | 0.614562i | \(0.789333\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.3739 | 1.23367 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.5826 | 1.13457 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.58258 | 0.803751 | 0.401876 | − | 0.915694i | \(-0.368358\pi\) | ||||
0.401876 | + | 0.915694i | \(0.368358\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.5826 | −2.13431 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.00000 | −0.307794 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 18.1652 | 1.82567 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.74773 | −0.770928 | −0.385464 | − | 0.922723i | \(-0.625959\pi\) | ||||
−0.385464 | + | 0.922723i | \(0.625959\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.0000 | 1.28093 | 0.640464 | − | 0.767988i | \(-0.278742\pi\) | ||||
0.640464 | + | 0.767988i | \(0.278742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.37386 | −0.817205 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.165151 | −0.0159658 | −0.00798289 | − | 0.999968i | \(-0.502541\pi\) | ||||
−0.00798289 | + | 0.999968i | \(0.502541\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −11.7477 | −1.12523 | −0.562614 | − | 0.826720i | \(-0.690204\pi\) | ||||
−0.562614 | + | 0.826720i | \(0.690204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.9564 | 1.32469 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.37386 | 0.787747 | 0.393873 | − | 0.919165i | \(-0.371135\pi\) | ||||
0.393873 | + | 0.919165i | \(0.371135\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7477 | −1.28198 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.79129 | −0.442955 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.79129 | −0.347547 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.37386 | 0.306715 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.5826 | −0.954199 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.74773 | −0.598764 | −0.299382 | − | 0.954133i | \(-0.596780\pi\) | ||||
−0.299382 | + | 0.954133i | \(0.596780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.58258 | −0.491518 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 22.1216 | 1.93277 | 0.966386 | − | 0.257095i | \(-0.0827653\pi\) | ||||
0.966386 | + | 0.257095i | \(0.0827653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.0000 | 1.29099 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.00000 | 0.512615 | 0.256307 | − | 0.966595i | \(-0.417494\pi\) | ||||
0.256307 | + | 0.966595i | \(0.417494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.74773 | −0.826791 | −0.413396 | − | 0.910551i | \(-0.635657\pi\) | ||||
−0.413396 | + | 0.910551i | \(0.635657\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −29.5390 | −2.48763 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.79129 | −0.317043 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.3739 | 0.944548 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.79129 | 0.230222 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.00000 | 0.245770 | 0.122885 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122885 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.3739 | −1.08835 | −0.544175 | − | 0.838972i | \(-0.683157\pi\) | ||||
−0.544175 | + | 0.838972i | \(0.683157\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 18.1652 | 1.46857 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −22.1216 | −1.77685 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.1216 | −1.60588 | −0.802939 | − | 0.596061i | \(-0.796731\pi\) | ||||
−0.802939 | + | 0.596061i | \(0.796731\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −23.3739 | −1.85367 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.58258 | 0.361158 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.37386 | −0.342587 | −0.171294 | − | 0.985220i | \(-0.554795\pi\) | ||||
−0.171294 | + | 0.985220i | \(0.554795\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 31.7477 | 2.47156 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −13.4174 | −1.03827 | −0.519136 | − | 0.854692i | \(-0.673746\pi\) | ||||
−0.519136 | + | 0.854692i | \(0.673746\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.79129 | −0.366399 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.7477 | 1.72948 | 0.864739 | − | 0.502222i | \(-0.167484\pi\) | ||||
0.864739 | + | 0.502222i | \(0.167484\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.00000 | −0.302372 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −33.9564 | −2.55232 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.7913 | 1.18030 | 0.590148 | − | 0.807295i | \(-0.299069\pi\) | ||||
0.590148 | + | 0.807295i | \(0.299069\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.37386 | −0.696754 | −0.348377 | − | 0.937355i | \(-0.613267\pi\) | ||||
−0.348377 | + | 0.937355i | \(0.613267\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.79129 | −0.206338 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 15.0000 | 1.10282 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.3739 | 1.05112 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.00000 | −0.363696 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.5390 | −1.70322 | −0.851612 | − | 0.524173i | \(-0.824374\pi\) | ||||
−0.851612 | + | 0.524173i | \(0.824374\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.37386 | 0.530782 | 0.265391 | − | 0.964141i | \(-0.414499\pi\) | ||||
0.265391 | + | 0.964141i | \(0.414499\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.37386 | −0.599665 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.37386 | −0.169131 | −0.0845654 | − | 0.996418i | \(-0.526950\pi\) | ||||
−0.0845654 | + | 0.996418i | \(0.526950\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.7477 | 1.68343 | 0.841716 | − | 0.539921i | \(-0.181546\pi\) | ||||
0.841716 | + | 0.539921i | \(0.181546\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 26.1652 | 1.84555 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.79129 | −0.266096 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3739 | −0.794385 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.9564 | −1.52608 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.79129 | −0.262249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.3739 | 1.67797 | 0.838983 | − | 0.544158i | \(-0.183151\pi\) | ||||
0.838983 | + | 0.544158i | \(0.183151\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 33.9564 | 2.32666 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.00000 | −0.409197 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.37386 | 0.500570 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 45.7042 | 3.08840 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.79129 | −0.255030 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7477 | 1.59027 | 0.795133 | − | 0.606435i | \(-0.207401\pi\) | ||||
0.795133 | + | 0.606435i | \(0.207401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 19.1652 | 1.27768 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.79129 | 0.251637 | 0.125818 | − | 0.992053i | \(-0.459844\pi\) | ||||
0.125818 | + | 0.992053i | \(0.459844\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.5826 | −0.696282 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −28.1216 | −1.84231 | −0.921153 | − | 0.389200i | \(-0.872752\pi\) | ||||
−0.921153 | + | 0.389200i | \(0.872752\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −31.7477 | −2.07099 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 27.9129 | 1.81314 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.74773 | 0.501159 | 0.250579 | − | 0.968096i | \(-0.419379\pi\) | ||||
0.250579 | + | 0.968096i | \(0.419379\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.74773 | −0.563491 | −0.281745 | − | 0.959489i | \(-0.590913\pi\) | ||||
−0.281745 | + | 0.959489i | \(0.590913\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16.1652 | −1.03699 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.00000 | 0.0636285 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −40.1216 | −2.54260 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.79129 | −0.618021 | −0.309010 | − | 0.951059i | \(-0.599998\pi\) | ||||
−0.309010 | + | 0.951059i | \(0.599998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −17.3739 | −1.09229 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 31.7477 | 1.98812 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.2087 | 0.699180 | 0.349590 | − | 0.936903i | \(-0.386321\pi\) | ||||
0.349590 | + | 0.936903i | \(0.386321\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.00000 | −0.310685 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 18.1652 | 1.12439 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.79129 | −0.418769 | −0.209384 | − | 0.977833i | \(-0.567146\pi\) | ||||
−0.209384 | + | 0.977833i | \(0.567146\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25.1216 | −1.54321 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 21.1652 | 1.29529 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.95644 | −0.607055 | −0.303527 | − | 0.952823i | \(-0.598164\pi\) | ||||
−0.303527 | + | 0.952823i | \(0.598164\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 14.1216 | 0.857826 | 0.428913 | − | 0.903346i | \(-0.358897\pi\) | ||||
0.428913 | + | 0.903346i | \(0.358897\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.79129 | 0.168936 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.1652 | 0.914493 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.25227 | 0.195410 | 0.0977051 | − | 0.995215i | \(-0.468850\pi\) | ||||
0.0977051 | + | 0.995215i | \(0.468850\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −35.3303 | −2.11517 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.4174 | 1.15835 | 0.579173 | − | 0.815205i | \(-0.303375\pi\) | ||||
0.579173 | + | 0.815205i | \(0.303375\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.37386 | 0.378887 | 0.189443 | − | 0.981892i | \(-0.439332\pi\) | ||||
0.189443 | + | 0.981892i | \(0.439332\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.37386 | −0.496025 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.79129 | 0.223793 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.62614 | −0.154479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −19.5390 | −1.14540 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.7477 | 1.15367 | 0.576837 | − | 0.816859i | \(-0.304287\pi\) | ||||
0.576837 | + | 0.816859i | \(0.304287\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −36.4955 | −2.12485 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 18.9564 | 1.09996 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.58258 | 0.265017 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | 0.115278 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −21.6261 | −1.24239 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.00000 | −0.171780 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.3739 | 1.56231 | 0.781154 | − | 0.624338i | \(-0.214631\pi\) | ||||
0.781154 | + | 0.624338i | \(0.214631\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 36.2867 | 2.06428 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −26.2087 | −1.48616 | −0.743080 | − | 0.669203i | \(-0.766636\pi\) | ||||
−0.743080 | + | 0.669203i | \(0.766636\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.7477 | 0.720544 | 0.360272 | − | 0.932847i | \(-0.382684\pi\) | ||||
0.360272 | + | 0.932847i | \(0.382684\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.3739 | −0.809875 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 14.8348 | 0.833208 | 0.416604 | − | 0.909088i | \(-0.363220\pi\) | ||||
0.416604 | + | 0.909088i | \(0.363220\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.3739 | 0.804782 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.460985 | −0.0257297 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.79129 | −0.210953 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.00000 | −0.221880 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −32.7913 | −1.81336 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.5826 | 0.583436 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.3739 | −1.55957 | −0.779784 | − | 0.626048i | \(-0.784671\pi\) | ||||
−0.779784 | + | 0.626048i | \(0.784671\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 23.9564 | 1.31280 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 28.1216 | 1.53645 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.37386 | 0.0748391 | 0.0374196 | − | 0.999300i | \(-0.488086\pi\) | ||||
0.0374196 | + | 0.999300i | \(0.488086\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.3739 | 1.26949 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −27.9564 | −1.51393 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −38.3739 | −2.06598 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.791288 | −0.0424786 | −0.0212393 | − | 0.999774i | \(-0.506761\pi\) | ||||
−0.0212393 | + | 0.999774i | \(0.506761\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.62614 | −0.0870451 | −0.0435225 | − | 0.999052i | \(-0.513858\pi\) | ||||
−0.0435225 | + | 0.999052i | \(0.513858\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.00000 | −0.266880 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.53901 | −0.454486 | −0.227243 | − | 0.973838i | \(-0.572971\pi\) | ||||
−0.227243 | + | 0.973838i | \(0.572971\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 36.4955 | 1.93698 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −10.5826 | −0.560089 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0.626136 | 0.0330462 | 0.0165231 | − | 0.999863i | \(-0.494740\pi\) | ||||
0.0165231 | + | 0.999863i | \(0.494740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.41742 | 0.494287 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 49.1216 | 2.57114 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.4955 | 1.17425 | 0.587127 | − | 0.809495i | \(-0.300259\pi\) | ||||
0.587127 | + | 0.809495i | \(0.300259\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −18.1652 | −0.945640 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.37386 | 0.434749 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.3739 | 0.847807 | 0.423903 | − | 0.905707i | \(-0.360660\pi\) | ||||
0.423903 | + | 0.905707i | \(0.360660\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.37386 | −0.432424 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.79129 | −0.195261 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.7477 | −1.11711 | −0.558553 | − | 0.829469i | \(-0.688643\pi\) | ||||
−0.558553 | + | 0.829469i | \(0.688643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.8348 | −0.964939 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −21.0000 | −1.07305 | −0.536525 | − | 0.843884i | \(-0.680263\pi\) | ||||
−0.536525 | + | 0.843884i | \(0.680263\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −11.3739 | −0.579666 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −9.58258 | −0.487110 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.6261 | −0.944383 | −0.472191 | − | 0.881496i | \(-0.656537\pi\) | ||||
−0.472191 | + | 0.881496i | \(0.656537\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −17.3739 | −0.878634 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 61.7477 | 3.11476 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 30.0000 | 1.50946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.25227 | −0.263604 | −0.131802 | − | 0.991276i | \(-0.542076\pi\) | ||||
−0.131802 | + | 0.991276i | \(0.542076\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.79129 | 0.139739 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12.6261 | −0.630519 | −0.315260 | − | 0.949005i | \(-0.602092\pi\) | ||||
−0.315260 | + | 0.949005i | \(0.602092\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.37386 | 0.367318 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.25227 | −0.0622259 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.9564 | 0.939636 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.1216 | 1.34108 | 0.670538 | − | 0.741875i | \(-0.266063\pi\) | ||||
0.670538 | + | 0.741875i | \(0.266063\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.7477 | 0.826104 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.1652 | 0.598608 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −43.1216 | −2.11676 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −27.2087 | −1.33242 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.7477 | 1.25786 | 0.628929 | − | 0.777462i | \(-0.283493\pi\) | ||||
0.628929 | + | 0.777462i | \(0.283493\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −50.7042 | −2.46532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.1652 | 0.735618 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.00000 | 0.0483934 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −10.5826 | −0.510932 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | 0.289010 | 0.144505 | − | 0.989504i | \(-0.453841\pi\) | ||||
0.144505 | + | 0.989504i | \(0.453841\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.74773 | 0.468446 | 0.234223 | − | 0.972183i | \(-0.424745\pi\) | ||||
0.234223 | + | 0.972183i | \(0.424745\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 31.7477 | 1.52219 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.58258 | 0.219214 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −41.4955 | −1.98047 | −0.990235 | − | 0.139408i | \(-0.955480\pi\) | ||||
−0.990235 | + | 0.139408i | \(0.955480\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.79129 | 0.228157 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.0436 | 0.667230 | 0.333615 | − | 0.942709i | \(-0.391732\pi\) | ||||
0.333615 | + | 0.942709i | \(0.391732\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.7477 | 1.07835 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 8.37386 | 0.396070 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.1216 | 1.18556 | 0.592781 | − | 0.805364i | \(-0.298030\pi\) | ||||
0.592781 | + | 0.805364i | \(0.298030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.3739 | −0.676839 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −37.3303 | −1.75393 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.00000 | 0.140642 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.8693 | −1.86501 | −0.932504 | − | 0.361160i | \(-0.882381\pi\) | ||||
−0.932504 | + | 0.361160i | \(0.882381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 18.9564 | 0.884811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.5390 | −0.537426 | −0.268713 | − | 0.963220i | \(-0.586598\pi\) | ||||
−0.268713 | + | 0.963220i | \(0.586598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.4955 | 1.60314 | 0.801570 | − | 0.597901i | \(-0.203998\pi\) | ||||
0.801570 | + | 0.597901i | \(0.203998\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −61.7477 | −2.86348 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −34.2867 | −1.58660 | −0.793301 | − | 0.608830i | \(-0.791639\pi\) | ||||
−0.793301 | + | 0.608830i | \(0.791639\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.37386 | −0.432845 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −56.1652 | −2.58795 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.58258 | −0.348647 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.00000 | −0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −40.1216 | −1.83704 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.6261 | −0.576903 | −0.288451 | − | 0.957495i | \(-0.593140\pi\) | ||||
−0.288451 | + | 0.957495i | \(0.593140\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00000 | −0.227980 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.7913 | 0.582024 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −21.0000 | −0.953561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | −0.498458 | −0.249229 | − | 0.968445i | \(-0.580177\pi\) | ||||
−0.249229 | + | 0.968445i | \(0.580177\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.2087 | −0.552097 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.1652 | 0.684394 | 0.342197 | − | 0.939628i | \(-0.388829\pi\) | ||||
0.342197 | + | 0.939628i | \(0.388829\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.3739 | 0.647366 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 54.4955 | 2.44939 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.1652 | −0.545682 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.6261 | −0.789054 | −0.394527 | − | 0.918884i | \(-0.629092\pi\) | ||||
−0.394527 | + | 0.918884i | \(0.629092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −37.4519 | −1.67323 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.33030 | 0.282254 | 0.141127 | − | 0.989991i | \(-0.454927\pi\) | ||||
0.141127 | + | 0.989991i | \(0.454927\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.2432 | −1.03431 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.4955 | −1.48759 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.330303 | 0.0146404 | 0.00732021 | − | 0.999973i | \(-0.497670\pi\) | ||||
0.00732021 | + | 0.999973i | \(0.497670\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3739 | −0.724337 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.00000 | −0.220755 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 39.0000 | 1.71855 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.1216 | −1.76455 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 63.4955 | 2.78714 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.4174 | −0.587828 | −0.293914 | − | 0.955832i | \(-0.594958\pi\) | ||||
−0.293914 | + | 0.955832i | \(0.594958\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.252273 | −0.0110311 | −0.00551556 | − | 0.999985i | \(-0.501756\pi\) | ||||
−0.00551556 | + | 0.999985i | \(0.501756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −11.1652 | −0.487287 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −27.9564 | −1.21780 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.00000 | −0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −58.2867 | −2.52943 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.79129 | 0.164219 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.495454 | −0.0214204 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 44.0780 | 1.90211 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.79129 | 0.163302 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −26.1652 | −1.12285 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −35.2432 | −1.50965 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 12.3739 | 0.529068 | 0.264534 | − | 0.964376i | \(-0.414782\pi\) | ||||
0.264534 | + | 0.964376i | \(0.414782\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.79129 | −0.204487 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.79129 | −0.161514 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.0000 | −0.425243 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 41.8693 | 1.77725 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.626136 | 0.0265303 | 0.0132651 | − | 0.999912i | \(-0.495777\pi\) | ||||
0.0132651 | + | 0.999912i | \(0.495777\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.00000 | 0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.1216 | 1.69393 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.1652 | 0.512700 | 0.256350 | − | 0.966584i | \(-0.417480\pi\) | ||||
0.256350 | + | 0.966584i | \(0.417480\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.1216 | 1.05687 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0.417424 | 0.0175302 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 30.1652 | 1.26459 | 0.632294 | − | 0.774728i | \(-0.282113\pi\) | ||||
0.632294 | + | 0.774728i | \(0.282113\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.4955 | −1.35989 | −0.679946 | − | 0.733262i | \(-0.737997\pi\) | ||||
−0.679946 | + | 0.733262i | \(0.737997\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −65.7042 | −2.74483 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.3303 | −0.764426 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.1216 | −0.962564 | −0.481282 | − | 0.876566i | \(-0.659829\pi\) | ||||
−0.481282 | + | 0.876566i | \(0.659829\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 20.5826 | 0.855383 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.3739 | 0.596328 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −31.7477 | −1.31486 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.3739 | −0.594286 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.16515 | 0.378286 | 0.189143 | − | 0.981950i | \(-0.439429\pi\) | ||||
0.189143 | + | 0.981950i | \(0.439429\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.37386 | 0.303835 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.62614 | −0.272563 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −28.9129 | −1.18731 | −0.593655 | − | 0.804720i | \(-0.702316\pi\) | ||||
−0.593655 | + | 0.804720i | \(0.702316\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.3739 | −0.466283 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 66.2867 | 2.71294 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.3739 | 0.832453 | 0.416227 | − | 0.909261i | \(-0.363352\pi\) | ||||
0.416227 | + | 0.909261i | \(0.363352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.6261 | 0.474240 | 0.237120 | − | 0.971480i | \(-0.423797\pi\) | ||||
0.237120 | + | 0.971480i | \(0.423797\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 44.9129 | 1.82899 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10.1216 | 0.411501 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26.4955 | −1.07542 | −0.537709 | − | 0.843131i | \(-0.680710\pi\) | ||||
−0.537709 | + | 0.843131i | \(0.680710\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −10.5826 | −0.428828 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.5826 | 0.428125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.3739 | 1.38835 | 0.694174 | − | 0.719808i | \(-0.255770\pi\) | ||||
0.694174 | + | 0.719808i | \(0.255770\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −31.7477 | −1.28019 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.95644 | −0.280056 | −0.140028 | − | 0.990148i | \(-0.544719\pi\) | ||||
−0.140028 | + | 0.990148i | \(0.544719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.37386 | −0.175800 | −0.0879002 | − | 0.996129i | \(-0.528016\pi\) | ||||
−0.0879002 | + | 0.996129i | \(0.528016\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.9129 | −0.919462 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.58258 | −0.303789 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.5826 | −0.422627 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 18.9564 | 0.755843 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25.0000 | 0.995234 | 0.497617 | − | 0.867397i | \(-0.334208\pi\) | ||||
0.497617 | + | 0.867397i | \(0.334208\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 68.0345 | 2.70413 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −20.2432 | −0.803326 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | −0.0396214 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 58.2867 | 2.30579 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.2087 | −0.798196 | −0.399098 | − | 0.916908i | \(-0.630677\pi\) | ||||
−0.399098 | + | 0.916908i | \(0.630677\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.0000 | −0.907031 | −0.453516 | − | 0.891248i | \(-0.649830\pi\) | ||||
−0.453516 | + | 0.891248i | \(0.649830\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.7477 | −0.659441 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 13.4174 | 0.527493 | 0.263747 | − | 0.964592i | \(-0.415042\pi\) | ||||
0.263747 | + | 0.964592i | \(0.415042\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −46.1216 | −1.81043 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.5826 | 0.806695 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 19.4174 | 0.759863 | 0.379931 | − | 0.925015i | \(-0.375948\pi\) | ||||
0.379931 | + | 0.925015i | \(0.375948\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 66.3648 | 2.59309 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 78.4519 | 3.06070 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 36.9564 | 1.43962 | 0.719809 | − | 0.694172i | \(-0.244229\pi\) | ||||
0.719809 | + | 0.694172i | \(0.244229\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.0000 | −1.32245 | −0.661223 | − | 0.750189i | \(-0.729962\pi\) | ||||
−0.661223 | + | 0.750189i | \(0.729962\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −10.5826 | −0.410993 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.00000 | 0.116335 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −17.3739 | −0.672719 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 66.2867 | 2.56279 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.79129 | −0.146361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.1216 | −0.659989 | −0.329994 | − | 0.943983i | \(-0.607047\pi\) | ||||
−0.329994 | + | 0.943983i | \(0.607047\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 20.0000 | 0.769800 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −21.9564 | −0.843855 | −0.421927 | − | 0.906630i | \(-0.638646\pi\) | ||||
−0.421927 | + | 0.906630i | \(0.638646\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.00000 | 0.268635 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.5826 | 0.405525 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 36.1652 | 1.38382 | 0.691911 | − | 0.721983i | \(-0.256769\pi\) | ||||
0.691911 | + | 0.721983i | \(0.256769\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.0000 | 0.687745 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −61.4083 | −2.34287 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.37386 | 0.319019 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −48.7477 | −1.85445 | −0.927225 | − | 0.374504i | \(-0.877813\pi\) | ||||
−0.927225 | + | 0.374504i | \(0.877813\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −18.1652 | −0.690037 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −29.2432 | −1.10926 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.3739 | −0.544449 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −78.4955 | −2.96897 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.3303 | 1.59879 | 0.799397 | − | 0.600804i | \(-0.205153\pi\) | ||||
0.799397 | + | 0.600804i | \(0.205153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.00000 | −0.188579 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −88.6170 | −3.33751 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.74773 | 0.291383 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.2432 | 1.17336 | 0.586681 | − | 0.809818i | \(-0.300434\pi\) | ||||
0.586681 | + | 0.809818i | \(0.300434\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47.9129 | 1.79687 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.7913 | 1.26549 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −11.3739 | −0.425358 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 21.6261 | 0.807643 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0000 | 0.447524 | 0.223762 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.0000 | −0.484145 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.4174 | −0.908094 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 15.1652 | 0.563220 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.0000 | −0.407967 | −0.203984 | − | 0.978974i | \(-0.565389\pi\) | ||||
−0.203984 | + | 0.978974i | \(0.565389\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −43.8693 | −1.62479 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.58258 | −0.280452 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 41.4955 | 1.53267 | 0.766335 | − | 0.642441i | \(-0.222078\pi\) | ||||
0.766335 | + | 0.642441i | \(0.222078\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.37386 | 0.308875 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 35.5390 | 1.30910 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.7477 | 1.31500 | 0.657501 | − | 0.753454i | \(-0.271614\pi\) | ||||
0.657501 | + | 0.753454i | \(0.271614\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.79129 | 0.102541 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −21.3303 | −0.782533 | −0.391266 | − | 0.920277i | \(-0.627963\pi\) | ||||
−0.391266 | + | 0.920277i | \(0.627963\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.00000 | 0.329734 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −68.8693 | −2.51980 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.165151 | 0.00603450 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.6261 | −0.424244 | −0.212122 | − | 0.977243i | \(-0.568037\pi\) | ||||
−0.212122 | + | 0.977243i | \(0.568037\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.3303 | −0.995972 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.1216 | −1.46017 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −48.4955 | −1.76027 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.3303 | −1.42572 | −0.712861 | − | 0.701305i | \(-0.752601\pi\) | ||||
−0.712861 | + | 0.701305i | \(0.752601\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.7477 | 0.425296 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 54.4955 | 1.97029 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.1652 | 0.439258 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4955 | −0.486659 | −0.243329 | − | 0.969944i | \(-0.578240\pi\) | ||||
−0.243329 | + | 0.969944i | \(0.578240\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.2867 | 1.12676 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 16.7477 | 0.602374 | 0.301187 | − | 0.953565i | \(-0.402617\pi\) | ||||
0.301187 | + | 0.953565i | \(0.402617\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −29.4955 | −1.05951 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −13.9564 | −0.500684 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.79129 | 0.135837 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 46.1216 | 1.65036 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 18.9564 | 0.677448 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.3648 | −2.15451 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.00000 | 0.142585 | 0.0712923 | − | 0.997455i | \(-0.477288\pi\) | ||||
0.0712923 | + | 0.997455i | \(0.477288\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −18.9564 | −0.674867 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.37386 | −0.297740 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.00000 | 0.0355110 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −70.1216 | −2.48696 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.8693 | −1.16429 | −0.582145 | − | 0.813085i | \(-0.697787\pi\) | ||||
−0.582145 | + | 0.813085i | \(0.697787\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −40.1216 | −1.41940 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.3303 | 1.28367 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 62.0780 | 2.19069 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.7477 | 0.484544 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −27.7913 | −0.978300 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −22.9129 | −0.805574 | −0.402787 | − | 0.915294i | \(-0.631958\pi\) | ||||
−0.402787 | + | 0.915294i | \(0.631958\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.4955 | 1.10595 | 0.552977 | − | 0.833196i | \(-0.313492\pi\) | ||||
0.552977 | + | 0.833196i | \(0.313492\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 39.4174 | 1.38243 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.1216 | −0.459629 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.00000 | 0.0699711 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.79129 | 0.167421 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.3303 | 1.47734 | 0.738669 | − | 0.674068i | \(-0.235455\pi\) | ||||
0.738669 | + | 0.674068i | \(0.235455\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 54.2432 | 1.89080 | 0.945399 | − | 0.325915i | \(-0.105672\pi\) | ||||
0.945399 | + | 0.325915i | \(0.105672\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 42.3303 | 1.47375 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −39.6606 | −1.37913 | −0.689567 | − | 0.724222i | \(-0.742199\pi\) | ||||
−0.689567 | + | 0.724222i | \(0.742199\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.00000 | −0.138926 | −0.0694629 | − | 0.997585i | \(-0.522129\pi\) | ||||
−0.0694629 | + | 0.997585i | \(0.522129\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.07803 | 0.314913 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.79129 | 0.131360 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −40.2523 | −1.39299 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −36.8693 | −1.27439 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.83485 | −0.305013 | −0.152506 | − | 0.988302i | \(-0.548734\pi\) | ||||
−0.152506 | + | 0.988302i | \(0.548734\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.6261 | −0.504350 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.1996 | 1.86673 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −36.0000 | −1.23844 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.37386 | −0.115927 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.7913 | 0.610595 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.9129 | −0.785443 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.12159 | 0.312317 | 0.156159 | − | 0.987732i | \(-0.450089\pi\) | ||||
0.156159 | + | 0.987732i | \(0.450089\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −14.3739 | −0.491576 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.7042 | −0.399807 | −0.199903 | − | 0.979816i | \(-0.564063\pi\) | ||||
−0.199903 | + | 0.979816i | \(0.564063\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.37386 | −0.251593 | −0.125796 | − | 0.992056i | \(-0.540149\pi\) | ||||
−0.125796 | + | 0.992056i | \(0.540149\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 10.5826 | 0.360653 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7042 | 1.31751 | 0.658753 | − | 0.752360i | \(-0.271084\pi\) | ||||
0.658753 | + | 0.752360i | \(0.271084\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 68.2432 | 2.32034 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.33030 | −0.248950 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 37.9129 | 1.28611 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9.37386 | −0.317621 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −33.5390 | −1.13512 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.00000 | 0.101419 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.7477 | −1.30842 | −0.654209 | − | 0.756314i | \(-0.726998\pi\) | ||||
−0.654209 | + | 0.756314i | \(0.726998\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 55.1216 | 1.85921 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.37386 | 0.0799775 | 0.0399887 | − | 0.999200i | \(-0.487268\pi\) | ||||
0.0399887 | + | 0.999200i | \(0.487268\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2523 | −0.816154 | −0.408077 | − | 0.912948i | \(-0.633801\pi\) | ||||
−0.408077 | + | 0.912948i | \(0.633801\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −101.869 | −3.42430 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −4.58258 | −0.153868 | −0.0769339 | − | 0.997036i | \(-0.524513\pi\) | ||||
−0.0769339 | + | 0.997036i | \(0.524513\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.74773 | 0.226312 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.58258 | −0.0530183 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.5826 | 0.354132 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.3739 | 1.58353 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 12.7913 | 0.427089 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.9564 | −0.932399 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7477 | −1.05767 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.58258 | 0.185776 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.1216 | −0.934793 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.2432 | −1.03741 | −0.518706 | − | 0.854952i | \(-0.673586\pi\) | ||||
−0.518706 | + | 0.854952i | \(0.673586\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −37.1216 | −1.23125 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.49545 | −0.115810 | −0.0579048 | − | 0.998322i | \(-0.518442\pi\) | ||||
−0.0579048 | + | 0.998322i | \(0.518442\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −54.4955 | −1.80354 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.37386 | −0.276831 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −22.1216 | −0.730519 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 34.4955 | 1.13790 | 0.568950 | − | 0.822372i | \(-0.307350\pi\) | ||||
0.568950 | + | 0.822372i | \(0.307350\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 76.4083 | 2.51774 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −12.1652 | −0.400421 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 20.0000 | 0.657596 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 62.2867 | 2.04577 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 47.8693 | 1.57054 | 0.785271 | − | 0.619153i | \(-0.212524\pi\) | ||||
0.785271 | + | 0.619153i | \(0.212524\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.00000 | −0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −73.1561 | −2.39502 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 43.1216 | 1.41023 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15.3739 | −0.502242 | −0.251121 | − | 0.967956i | \(-0.580799\pi\) | ||||
−0.251121 | + | 0.967956i | \(0.580799\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.5826 | 1.16119 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.4955 | 0.896326 | 0.448163 | − | 0.893952i | \(-0.352078\pi\) | ||||
0.448163 | + | 0.893952i | \(0.352078\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.3739 | 0.565771 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −15.0000 | −0.487950 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.6170 | 1.70982 | 0.854912 | − | 0.518773i | \(-0.173611\pi\) | ||||
0.854912 | + | 0.518773i | \(0.173611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −16.3739 | −0.531518 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 41.4083 | 1.34276 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 21.4610 | 0.695189 | 0.347595 | − | 0.937645i | \(-0.386999\pi\) | ||||
0.347595 | + | 0.937645i | \(0.386999\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −70.6170 | −2.28511 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 40.1216 | 1.29695 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.00000 | −0.193750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3739 | 0.753996 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −0.791288 | −0.0254989 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.1216 | 0.712119 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1216 | −0.389804 | −0.194902 | − | 0.980823i | \(-0.562439\pi\) | ||||
−0.194902 | + | 0.980823i | \(0.562439\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.5826 | −0.339961 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.0000 | −0.481373 | −0.240686 | − | 0.970603i | \(-0.577373\pi\) | ||||
−0.240686 | + | 0.970603i | \(0.577373\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.74773 | 0.312498 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.1652 | −0.357571 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −34.4174 | −1.10111 | −0.550555 | − | 0.834799i | \(-0.685584\pi\) | ||||
−0.550555 | + | 0.834799i | \(0.685584\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 28.7477 | 0.918781 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −56.2867 | −1.79710 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −8.66970 | −0.276520 | −0.138260 | − | 0.990396i | \(-0.544151\pi\) | ||||
−0.138260 | + | 0.990396i | \(0.544151\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.12159 | −0.226913 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 29.5390 | 0.940237 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.16515 | 0.291435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.74773 | 0.277881 | 0.138940 | − | 0.990301i | \(-0.455630\pi\) | ||||
0.138940 | + | 0.990301i | \(0.455630\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −79.1996 | −2.51332 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 71.2432 | 2.25856 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.87841 | −0.0911601 | −0.0455801 | − | 0.998961i | \(-0.514514\pi\) | ||||
−0.0455801 | + | 0.998961i | \(0.514514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 25.0000 | 0.790965 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 2128.2.a.k.1.2 | 2 | ||
4.3 | odd | 2 | 532.2.a.c.1.1 | ✓ | 2 | ||
8.3 | odd | 2 | 8512.2.a.t.1.2 | 2 | |||
8.5 | even | 2 | 8512.2.a.m.1.1 | 2 | |||
12.11 | even | 2 | 4788.2.a.g.1.2 | 2 | |||
28.27 | even | 2 | 3724.2.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
532.2.a.c.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
2128.2.a.k.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3724.2.a.e.1.2 | 2 | 28.27 | even | 2 | |||
4788.2.a.g.1.2 | 2 | 12.11 | even | 2 | |||
8512.2.a.m.1.1 | 2 | 8.5 | even | 2 | |||
8512.2.a.t.1.2 | 2 | 8.3 | odd | 2 |